If k=1/(1+2x), where x is an integer greater than 1 and k can be represented as a terminating decimal, find the sum of all possible values of k. Can anyone guide to me to find the solution for this problem?

Adrian Brown

Adrian Brown

Answered question

2022-11-04

If k = 1 1 + 2 x , where x is an integer greater than 1 and k can be represented as a terminating decimal, find the sum of all possible values of k. Can anyone guide to me to find the solution for this problem?

Answer & Explanation

tiulowyn9v

tiulowyn9v

Beginner2022-11-05Added 7 answers

Step 1
The decimal expansion of 1 n where n is an integer only terminates iff all prime factors of n are also prime factors of 10 - that is, if
n = 2 a 5 b
for some positive integers a,b.

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